research and comments on quantum physics of materials

Icing model

Lucile Savary and I just posted a paper on the arXiv on “Disorder induced entanglement” in spin ice systems. This was stimulated by experiments by Satoru Nakatsuji, Collin Broholm, and their collaborators on Pr2Zr2O7, which was supposed to be a type of “quantum spin ice”. The idea was that the exchange couplings between Pr spins would involve a lot of spin-flip interactions, which induce quantum dynamics. Their experiments revealed that actually disorder was more important than the quantum exchanges.

This turns out to be related to a bit of very common atomic physics. Pr3+ is what is called a non-Kramers ion, which means that it has an even number of electrons. It forms a two-level system which we can describe using a spin-1/2 operator like a Pauli matrix, but which is not quite a usual spin. In particular, for such a non-Kramers ion, the spin operator is not odd under time-reversal. Actually in this case the z component is odd, but the x and y components are even (this is equivalent to the condition T^2 = +1 that theorists like). As a consequence, disorder in the material, for example misplaced ions in the Zr sites, or missing/extra O, exert electric fields inside the sample that induce local random “transverse fields”, i.e. terms like h_x S^x +h_y S^y, with different h_x,h_y for each spin. This effect is electrostatic in origin, so it should be a robust and dominant one.

Schematic phase diagram of the random transverse field Icing model. See the preprint for an explanation.

A transverse field is a textbook way to induce quantum dynamics in a classical system. For example, the transverse field Ising ferromagnet is the paradigm for quantum criticality. What we learned is that in non-Kramers systems, a transverse field can be induced without any real magnetic field, even without breaking time-reversal symmetry. So we thought: let’s put this to work for us! One should be able to controllably induce quantum dynamics by introducing disorder in an otherwise classical magnet. The spin ice pyrochlores are a natural place to look. The two most studied materials are Dy2Ti2O7 and Ho2Ti2O7. Both seem to be modeled extremely well by a classical Ising model. Dy3+ is a Kramers ion, so it does not work for us, but Ho3+ is a non-Kramers ion, so we’re in business! A good model for disordered Ho2Ti2O7 is thus the classical spin ice Ising model plus a local random transverse field. Inspired by the textbooks, we called this the random field Icing model.

Yes, the entire post has been a set up for the name. I’m really proud of it. The physics is pretty interesting too. You can read about in the arXiv article. That’s the original text – we’ve had to cut it since to fit journal length constraints, in our rather long and painful referee process which is still on-going (I don’t understand why so many referees are so bitter – lighten up!). We rather like the original text which is more pedagogical.